Problem: A circle has a sector with area $20\pi$ and central angle $72^\circ$. What is the area of the circle? ${100\pi}$ $\color{#9D38BD}{72^\circ}$ ${20\pi}$
Solution: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{72^\circ}{360^\circ} = 20\pi \div A_c$ $\dfrac{1}{5} = 20\pi \div A_c$ $A_c \times \dfrac{1}{5} = 20\pi$ $A_c = 20\pi \times 5$ $A_c = 100\pi$